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Umaxo
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In general relativity there is (in general) only local conservation of energy, i.e. theglobal conservation of energy is conserved onlydoes not exist the way it does in small neigbourhoods, where the curvaturerest of spacetimethe physics. That is neglectable and spacetime candue to the difficulties in defining gravitational energy, which cannot really be considered that of special theory of relativitydone "correctly". But when

However you consider larger areascan define gravitational energy "uncorrectly" (f.e. using Landau-Lifshitz pseudotensor), in which case the conservation of energy is not conservedwill seemingly hold and light will loose its energy to gravitational part of the overall energy.

In general relativity there is only local conservation of energy, i.e. the energy is conserved only in small neigbourhoods, where the curvature of spacetime is neglectable and spacetime can be considered that of special theory of relativity. But when you consider larger areas, the energy is not conserved.

In general relativity there is (in general) only local conservation of energy, global conservation of energy does not exist the way it does in the rest of the physics. That is due to the difficulties in defining gravitational energy, which cannot really be done "correctly".

However you can define gravitational energy "uncorrectly" (f.e. using Landau-Lifshitz pseudotensor), in which case the conservation of energy will seemingly hold and light will loose its energy to gravitational part of the overall energy.

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Umaxo
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In general relativity there is only local conservation of energy, i.e. the energy is conserved only in small neigbourhoods, where the curvature of spacetime is neglectable and spacetime can be considered that of special theory of relativity. But when you consider larger areas, the energy is not conserved.